Vitamin K is the essential vitamin involved in the process of blood coagulation. It plays a critical role in the synthesis of specific proteins known as clotting factors, which are produced in the liver.
These clotting factors, such as prothrombin (Factor II), are necessary for the proper formation of blood clots. Without adequate Vitamin K, the blood clotting process is impaired, which can lead to excessive bleeding even from minor injuries.
Thus, Vitamin K is indispensable for maintaining hemostasis and preventing hemorrhagic conditions.
A racing track is built around an elliptical ground whose equation is given by \[ 9x^2 + 16y^2 = 144 \] The width of the track is \(3\) m as shown. Based on the given information answer the following: 
(i) Express \(y\) as a function of \(x\) from the given equation of ellipse.
(ii) Integrate the function obtained in (i) with respect to \(x\).
(iii)(a) Find the area of the region enclosed within the elliptical ground excluding the track using integration.
OR
(iii)(b) Write the coordinates of the points \(P\) and \(Q\) where the outer edge of the track cuts \(x\)-axis and \(y\)-axis in first quadrant and find the area of triangle formed by points \(P,O,Q\).